MR2538280
Yasuhiko YAMADA
Yasuhiko YAMADA
Padé Method to Painlevé Equations
Funkcialaj Ekvacioj. Serio Internacia
52
2009
83--92
http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-1/52_83.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2538280
A class of special solutions of Painlevé/Garnier systems arising as the Bäcklund or Schlesinger transformations of the Riccati solutions is known. In the past several years, the corresponding $\tau$-functions have been explicitly computed and expressed as certain specialization of the Schur functions with rectangle shape partitions. In this note, we will give a simple and direct derivation of these solutions. Our method is based on the Padé approximation and its intrinsic relation to iso-monodromy deformations.
Painlevé equation, Padé approximation, Schur function, Garnier system, Iso-monodromy deformation.
34A05, 34A34, 41A21.
52-83
2009
Padé Method to Painlevé Equations
Yasuhiko YAMADA
Yasuhiko YAMADA
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